Coat cold cooking grate of grill with cooking spray, and place on grill. Preheat grill to 350° (medium) heat.
Peel shrimp, and slice in half lengthwise; devein, if desired.
Sauté onion, bell pepper, salt, and pepper in 1/2 tsp. hot oil in a large skillet over medium heat 5 minutes or until tender. Transfer onion mixture to a large bowl. Sauté shrimp in remaining 1 tsp. hot oil 3 minutes or just until shrimp turn pink. Add shrimp to onion mixture, and toss.
Divide dough into 6 equal portions. Lightly sprinkle flour on a large surface. Roll each portion into a 6-inch round (about 1/4-inch thick). Carefully transfer pizza dough rounds to a cutting board or baking sheet sprinkled with cornmeal.
Slide pizza dough rounds onto cooking grate of grill; spread Garden Pesto over rounds, and top with shrimp mixture. Sprinkle each with 2 Tbsp. Parmesan cheese.
Grill, covered with grill lid, 4 minutes. Rotate pizzas one-quarter turn, and grill, covered with grill lid, 5 to 6 more minutes or until pizza crusts are cooked. Serve immediately.
*Refrigerated store-bought pesto may be substituted.
Note: Individual pizza dough rounds may be made ahead. Roll out as directed, and place between pieces of wax paper sprinkled with flour and cornmeal; place in a gallon-size zip-top plastic bag. Seal bag, and chill 8 hours.